Interesting that jego does not decline.
Yup, it makes life a little bit easier. Same goes for "jej" (her) and "ich" (their).
Why is is this muzyka and not muzyki?
It is a normal, simple nominative sentence ([noun] is [adjective]) such as "Film jest nudny".
What about "jego muzyka to nudna"?
Nope, doesn't work. You can only use the 'to' construction if there are noun phrases on both sides.